Love, Hate and Complex Numbers

Love is, one of, if not the most powerful emotion. It pushes us to extremes. When in love you will do next to anything for a person. No mountain seems too high to climb, no valley too dark to venture though. A person fueled by love can achieve a lot.

But what is the true opposite of love? Many would say hate. But what is hate, exactly? To me the threshold to hate is simple: Are you willing to -realistically- go to someones funeral and laugh at them or urinate on their grave? If not, maybe you are just really irritated or spiteful. So, hate can bring out the strength in us to do horrible things. Quite the polar opposite what love does.

But hate,let´s us conquer same obstacles, like the metaphorical mountains love let is easily overcome if fueled by it.

So maybe, like other philosophers on the internet have already stated, love and hate are not so different, after all. Maybe the true antithesis to both love and hate is indifference.

Only indifference truly stops us from achieving greatness, whatever that may be in the situation.

The thought:” Eh, maybe it´s not worth doing it” dampens our enthusiasm. Of course too much of it can lead to apathy, where only a strong emotion like hate or love can get us back into excitement.

This is model how love works is not incorrect, but incomplete. Emotions are not on numbers on a ray. They are vectors.

What we need to completely understand love and hate is an Argand Diagram, also known as a complex number plane.

Z= x+y*j

Z being our emotion, x the level of excitement and y the goodness of our actions.

Just like emotions, complex numbers cannot be measured which one is bigger. However, we can calculate their strength. We need to use the formula:

|Z|=sqrt([x^2] +[y^2])

For example:

If you are +9eu excited for a person and do an action that´s +4gu , then your emotion has the strength of

|Z| = sqrt(3²+4²)

= sqrt(9+16)

= sqrt(25)

= 5

(eu:=excitement unit, gu:=goodness unit)

Furthermore, this model does also explain the motivation behind, and result of both rage sex(crudely known as “hate fucking”) and makeup sex.

Both types of intercourse rely on the fact that loves´ and hates´ amount of excitement in Z.

Adding these vectors amplifies the result. Based on these calculations we can reasonably assume the outcome of said interaction.

If person A has Z1 = 3eu + 4gu and person B Z2= 7eu + 2gu ,the resulting complex number would be:


Zr1 = Z1 + Z2

=(3eu + 4gu) + (7eu + 2gu)

=10eu + 2gu

|Zr1| = sqrt(10² + 2²)

= sqrt(104)


=10.2 (rounded)


Zr2 = 4eu +3gu , Z4=2eu - 7gu

= Z3 + Z4

= (4eu + 3gu) + (2eu – 7gu)

= 6eu – 4gu

|Zr2| = sqrt(6² + (-4)²)

= sqrt(36 +16)

= sqrt(52)


= 7.21 (rounded)

Therefore, the intercourse between a moderately good and exciting person and a very exciting but morally tame person is bound to be very exciting. Two similarly exciting people who are very different on the goodness scale have mathematically less strong emotional connection. A long time relationship is less likely.

The most healthy relationships would be the ones sharing a quadrant, be quadrant II, where it is rather boring and morally good or quadrant IV, where it is morally questionable but exciting.

(Though this one might be better for the relationship itself than society at large.)

An even more accurate model would include a third axis, where one records whether the emotion is altruistic or egocentric in nature. But, for the sake of brevity and simplicity that is going to be in another post.

In conclusion, love and hate are not diametrically opposed. They are more complex (pun intend) than that. Once you have your excitement- and goodness units defined, it becomes an exercise of mathematics to decide whether you actually have such a strong emotional bond to that thing, if you cannot get off the couch for it or not. Similarly you can now use the power of math to make an educated guess if make up sex will lead to saving the relationship or if it is not worth the hassle.

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Nur ein kleiner Bär der versucht eine große Welt zu verstehen.

I´d call this philosophy if I thought it was good
I´d call this philosophy if I thought it was good

Just random thoughts that I cannot get out of my head if I don´t write them down and share with the world.

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